Bring a large pot of water to a rolling boil, add salt, and cook the pasta to al dente according to the package instructions. Reserve a 1/2 cup of pasta water.

Meanwhile, heat a large skillet to medium heat and drizzle in enough olive oil to coat the bottom (2-3 tablespoons). Cook chicken about 4 minutes per side, flipping once. During the last 1-2 minutes of cook time, add in 2 teaspoons of minced garlic and saute with the chicken. Set aside under tented foil.

In the same skillet over low heat, add a little more olive oil and the remaining garlic, saute for 30 seconds, then add the spinach. Use tongs to toss the spinach to ensure it cooks evenly, cooking about 2-3 minutes or until it's wilted.

In a large bowl, combine pesto, capers, red pepper flakes, lemon juice and zest, 1 cup parmesan, and 1/4 cup pasta water. Stir until it comes together into a sauce. Fold in the spinach, pasta, and chicken, along with the remaining parmesan and pasta water. Toss everything together until it's evenly coated. Taste and sprinkle with a bit of salt and pepper if needed.